Topological Defects 18.354 L24 Order Parameters, Broken Symmetry, - PowerPoint PPT Presentation

Mar 24, 2023 •39 likes •249 views

Topological Defects 18.354 L24 Order Parameters, Broken Symmetry, and Topology James P. Sethna Laboratory of Applied Physics, Technical University of Denmark, DK-2800 Lyngby, DENMARK, and NORDITA, DK-2100 Copenhagen , DENMARK and Laboratory

Topological Defects 18.354 L24 Order Parameters, Broken Symmetry, and Topology James P. Sethna Laboratory of Applied Physics, Technical University of Denmark, DK-2800 Lyngby, DENMARK, and NORDITA, DK-2100 Copenhagen Ø, DENMARK and Laboratory of Atomic and Solid State Physics (LASSP), Clark Hall, Cornell University, Ithaca, NY 14853-2501, USA (Dated: May 27, 2003, 10:27 pm) dunkel@mit.edu
• work hardening, etc • optical effects order-parameter fields are discontinuities in Topological defects "umbilic defects" in a nematic liquid crystal
order = symmetry = invariance � (under certain group actions ) symmetry groups can be discrete, continous, Lie-groups, ….
More or less symmetric ?
More or less symmetric ? Mg 2 Al 4 Si 5 O 18 http://www.doitpoms.ac.uk/tlplib/crystallography3/printall.php
More or less symmetric ? broken continuous translation/rotation symmetry (invariance)
Order parameters: 2D crystal 4 � dx ( κ / 2)( du/dx ) 2 . E = u + a ˆ x = ⃗ u + ma ˆ x + na ˆ ⃗ u ≡ ⃗ y.
Order parameters: magnets tant.
Order parameters: nematic liquid crystals “projective plane” = half-sphere with opposite points on equator identified
Topological defects
Work hardening
Disclinations edge screw
Disclineations
Bacterial vortices PIV +1 -1 -1 +1 Dunkel et al PRL 2013
Active nematics Dogic lab (Brandeis) Nature 2012
Active nematics Giomi et al PRL 2012
Defects in nematics winding number
Defects in nematics winding number
Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects Igor Musevic et al. Science 313 , 954 (2006); DOI: 10.1126/science.1129660 s bilized ). taneously geometric l- col- p fabrication loids re- l- ecision micro- a- ce d s. ic id
Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects Igor Musevic et al. Science 313 , 954 (2006); DOI: 10.1126/science.1129660
Reconfigurable Knots and Links in Chiral Nematic Colloids Uros Tkalec et al. Science 333 , 62 (2011); DOI: 10.1126/science.1205705 efect ts s. g nt rs a he on e ori- o- Defect dimer, re nknot. e topologi- o loops. d- ns numerical- u-de el l- nd r- the fu- are by using a program for representing knots ( 33 ) to show the relaxation

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